To show the advantages and the different implications of our approach, blackwe compare our results with the ones obtained by considering each asset separately, as if we ignored their possible dependence structure. Specifically, the three CAViaR models are estimated individually for each stock market index using the univariate approach of [1]}. To assess the performance of the three models and to combine the individual forecasts of the three indices in a single value, we use the sum of the three corresponding AL log scores (see [1]}) as consistent scoring rule. That is, at each time \(t\) , and for each model \(j\) , we define the following scoring function:
\(S_{AL_{t}}^{(j)}(\tau ) = \sum _{p=1}^3 S_{AL_{p,t}}^{(j)}(\tau _p)\) 
